Radiation resistance

Radiation resistance is that part of an antenna's feedpoint resistance that is caused by the radiation of electromagnetic waves from the antenna. The radiation resistance is determined by the geometry of the antenna, not by the materials of which it is made. It can be viewed as the equivalent resistance to a resistor in the same circuit.

Radiation resistance is caused by the radiation reaction of the conduction electrons in the antenna.

When electrons are accelerated, as occurs when an AC electrical field is impressed on an antenna, they will radiate electromagnetic waves. These waves carry energy that is taken from the electrons. The loss of energy of the electrons appears as an effective resistance to the movement of the electrons, analogous to the ohmic resistance caused by scattering of the electrons in the crystal lattice of the metallic conductor.

While the energy lost by ohmic resistance is converted to heat, the energy lost by radiation resistance is converted to electromagnetic radiation.

Power is calculated as

: $P\; =\; I^2R$

where $I$ is the electric current flowing into the feeds of the antenna and $P$ is the power in the resulting electromagnetic field. The result is that there is a virtual, effective resistance:

: $R\; =\; frac\{P\}\{I^2\}.$ This effective resistance is called the radiation resistance.

Thus the radiation resistance of an antenna is a good indicator of the strength of the electromagnetic field radiated by a transmitting antenna or being received by a receiving antenna, since its value is directly proportional to the "power" of the field.

Useful formulas

Electromagnetic theory [Edward C. Jordan, Keith G Balmain, "Electromagnetic Waves and Radiating Systems", 2nd. Ed., Prentice-Hall Inc., 1968, LOCC68-16319, pp. 325-326] employs Maxwell's equations on a very small piece of the length of an antenna to determine the behavior of that small increment and then uses Integration to aggregate the behavior to that of the entire antenna. As result the derivation gives the radiation resistance of a small (less than a quarter wavelength) dipole antenna as

: $R\; =\; 20pi^2left(frac\{ell\}\{lambda\}\; ight)^2$

where $ell$ is the length of the antenna in meters, $lambda$ is the wavelength of the signal in meters, and $R$ is measured in ohms.

It is also shown that the radiation resistance of a small monopole (of height $h$) over a ground plane is

: $R\; =\; 40pi^2left(frac\{h\}\{lambda\}\; ight)^2.$

Consider a monopole whose height $h$ is half the overall length $ell$ of a dipole. Substituting

: $h\; =\; frac\; \{ell\}\; \{2\}$

results in

: $R\; =\; 40pi^2left(frac\{frac\; \{ell\}\; \{2\{lambda\}\; ight)^2$: $=\; 40pi^2left(frac\{ell\}\; \{2cdotlambda\}\; ight)^2$ : $=\; 40frac\{pi^2\}\{4\}cdotleft(frac\{ell\}\; \{lambda\}\; ight)^2$

or

: $R\; =\; 10pi^2cdotleft(frac\{ell\}\; \{lambda\}\; ight)^2.$

Thus as expected the radiation resistance of a monopole half the size of a dipole will be half the radiation resistance of the dipole.

Extending the mathematics to quarter and half wavelength antennas [Edward C. Jordan, Keith G Balmain, "Electromagnetic Waves and Radiating Systems", 2nd. Ed., Prentice-Hall Inc., 1968, LOCC68-16319, p. 332] shows that:

* The radiation resistance of a quarter wave monopole over a ground plane is 36.5 ohms.

* The radiation resistance of a half wave dipole over a ground plane is 73 ohms.

References

ee also

*Abraham-Lorentz force